A variety of statistical methods that provide a basis for climate change research have been developed and examined. In the analysis of trends in climate elements, parametric (least-squares regression) and non-parametric (median of pairwise slopes) methods have been compared. The two methods yield trend magnitudes that differ only marginally even for non-normally distributed variables; the difference between the trend estimates does not depend on the degree of normality of the variable. Extreme value analysis (employing the ‘annual maxima’ method with the Generalized Extreme Value distribution, and a stochastic modelling with the first order autoregressive model) was used to study extreme temperature events in climate model outputs, and return period of severe heat waves (observed in 1994) and record breaking summer one-day temperature (1983). Various parameter estimation approaches were compared, with a special concern devoted to the maximum likelihood and L-moment methods. Methods of non-linear time series analysis were applied to time series of rock slope movements to study the rock slope dynamics. Nonequidistant records of dilatometric measurements of relative displacements on rock cracks on stable and unstable sandstone slopes (NW Bohemia – Hřensko) have been analysed and tested for possible nontrivial (e.g. nonlinear and deterministic) dynamics. Simultaneously, time series of meteorological parameters (temperature, precipitation, humidity) recorded at the nearest stations were tested in search for their possible effects on studied rock slope dynamics. In the statistical downscaling, which consists in looking for statistical relationships between large-scale upper-air variables with the local surface ones, research concentrates on the sensitivity of climate change estimates to the selection of the downscaling model and predictors. Stochastic weather generator Met&Roll is being used for creating synthetic daily weather series (precipitation, extreme temperatures, solar radiation) whose statistical properties reproduce the observed series, and can be easily modified in order to simulate weather under changed climatic conditions. The generator was modified substantially; firstly, additional daily (e.g. wind, humidity) weather variables could be generated by nearest neighbours resampling, secondly, the synthetic weather series might follow up with the observed series at any day of the year and fit the long-term weather forecast. The modifications were inspired by needs of so-called PERUN system designed to provide seasonal forecast of crop yields. The improved generator has been used widely in assessments of climate change impacts. Five versions of the weather generator were evaluated as to their ability to reproduce heat and cold waves and extreme high and low one-day temperatures at more than 80 locations covering most of Europe. Furthermore, we have examined the effects various methodological options have on the detection of modes of variability by means of principal component analysis. In particular, the choice of the similarity matrix (correlation or covariance), type of grid (latitude-longitude or equal-area), and rotation of principal components affect the resulting patterns. Specifically, the North Atlantic Oscillation (NAO) should be preferred to the Arctic Oscillation (AO) in describing the leading mode of variability in the Northern Hemisphere.